1. Field of the Invention
The present invention relates to an apparatus and a method for controlling the driving of a body in which, in a case where an object body is moved at a high speed and is stopped at an accurate position as in controlling the tilting motion of an auxiliary mirror in a reflecting telescope, controlling an arm in a high-speed robot, or controlling such as a stepper, i.e., an apparatus for manufacturing a semiconductor, a compensating body is supported by a support so as to eliminate a reaction force occurring in the support for supporting the object body due to the movement of the body, and the object body and the compensating body are made to undergo motion with opposite phases, thereby allowing the reaction force occurring in the support due to the motion of the object body and the reaction force occurring in the support due to the motion of the compensating body to offset each other, so as to prevent an unnecessary force from being imparted to the support.
In particular, a description will be given of an example in which the apparatus and the method for controlling the driving of a body in accordance with the present invention is applied to an apparatus and a method for controlling the driving of an auxiliary mirror wherein in a case where an image observed with a reflecting telescope includes background noise, an auxiliary mirror which receives incident light from a main mirror is inclined at high speed and with high accuracy to a predetermined angle with respect to a reference plane, so as to eliminate or reduce the background noise.
2. Description of the Related Art
When a celestial body is observed by using a reflecting telescope, an image which is observed usually includes background noise due to the effect of the fluctuation of the atmosphere and the like. A spatial chopping method is known as one of the methods for eliminating or reducing such noise.
The spatial chopping method is a method whereby an image which includes the background noise and an image which includes only the background noise are alternately observed, and a difference between the two images is determined, so as to eliminate or reduce the background noise.
Specifically, in order to alternately observe the image which includes the background noise and the image which includes only the background noise, it is necessary to displace the angle of the auxiliary mirror to a predetermined angle.
The basic principle of displacing the angle of the auxiliary mirror is shown in FIGS. 13A and 13B and FIG. 14. In FIGS. 13A and 13B, reference numeral 10 denotes an auxiliary mirror, which is located inside the telescope.
In addition, in FIGS. 13A and 13B, the dotted line denotes a reference plane which serves as a reference at a time when the angle (inclination) of the auxiliary mirror 10 is measured. Normally, the ground, a main mirror (not shown) fixed inside the reflecting telescope, or the like is set as the reference plane. In addition, when the inclination of the auxiliary mirror 10 is parallel with the reference plane, the angle of the auxiliary mirror 10 is 0.
FIG. 13A is a diagram illustrating a state when the angle of the auxiliary mirror 10 is .theta..sub.1, while FIG. 13B is a diagram illustrating a state when the angle of the auxiliary mirror 10 is .theta..sub.2.
Further, FIG. 14 is a diagram illustrating the characteristic of the angle of displacement of the auxiliary mirror 10 with respect to a change over time.
To alternately observe the image which includes the background noise and the image which includes only the background noise, when the angle of the auxiliary mirror 10 is, for instance, .theta..sub.1, after the auxiliary mirror 10 is held at this position for a time duration T.sub.1 sufficient for the observation of the image which includes the background noise, the auxiliary mirror 10 is displaced up to an angle .theta..sub.2 for a time duration T.sub.3. Then, after the auxiliary mirror 10 is held at this position for a time duration T.sub.2 sufficient for the observation of the image which includes only the background noise, the auxiliary mirror 10 is displaced up to the angle .theta..sub.1 for a time duration T.sub.4.
If the image which includes the background noise and the image which includes only the background noise are observed alternately by repeating the above-described operation periodically, and if a difference between the two images is determined, it is possible to eliminate or reduce the background noise which is included during the observation.
As shown in FIG. 14, the change of the angle of displacement of the auxiliary mirror 10 with respect to time exhibits periodicity, and is generally designed such that .theta..sub.1 =-.theta..sub.2, T.sub.1 =T.sub.2, and T.sub.3 =T.sub.4.
Since the position of the celestial body and the fluctuation of the atmosphere change over time, the time required for alternately observing the image which includes the background noise and the image which includes only the background noise should preferably be made as short as possible.
For this reason, the time durations T.sub.3 and T.sub.4 should preferably be made as short as possible.
In addition, there has been a problem in that the background noise cannot be eliminated unless the auxiliary mirror is held accurately at the position of the angle of displacement .theta..sub.1 or .theta..sub.2 without vibrating while the images are being observed.
A conventional apparatus for driving an auxiliary mirror devised to overcome the above-described problem is shown in FIG. 15.
FIG. 15 is a cross-sectional view illustrating the structure of a conventional apparatus for driving an auxiliary mirror which is disclosed in U.S. Pat. No. 5,099,352 and was developed for the purpose of tilting and angularly displacing the auxiliary mirror of an optical telescope, though by a very small amount, at high speed and with high accuracy.
In FIG. 15, reference numeral 10 denotes the auxiliary mirror; 11, a dynamically compensating balancer; 50, an actuator for driving the auxiliary mirror 10; 15, a hinge for rotating the auxiliary mirror 10 by a very small amount; 16, a hinge for rotating the dynamically compensating balancer 11 by a very small amount; 12, a mounting base for fixing the auxiliary mirror 10 and the dynamically compensating balancer 11 by means of the hinges 15 and 16; 51, an actuator for driving the dynamically compensating balancer 11; 52, an angle sensor for detecting the angle of the auxiliary mirror 10; and 53, an angle sensor for measuring the angle of the dynamically compensating balancer 11 with respect to the mounting base 12.
Next, a description will be given of the operation.
In a case where the dynamically compensating balancer 11 is not present, when the auxiliary mirror 10 is rotatively driven, the mounting base 12 is swayed in an opposite direction to the rotating direction of the auxiliary mirror 10 owing to its reaction (hereafter, a force occurring in the mounting base 12 due to this reaction will be referred to as a driving reaction force). As a result, the mounting base 12 tilts.
Consequently, the angle between the auxiliary mirror 10 and the mounting base 12 becomes different from that intended by a designer, so that the accuracy of displacement deteriorates.
Accordingly, to avoid the above-described drawback, the dynamically compensating balancer 11 having a shape and mass which are substantially equivalent to those of the auxiliary mirror 10 is conventionally driven with an opposite phase to that of the auxiliary mirror 10, so as to make the mounting base 12 stationary.
That is, the swaying of the mounting base 12 is controlled by designing such that the driving reaction force occurring in the mounting base 12 due to the rotation of the dynamically compensating balancer 11 and the driving reaction force occurring in the mounting base 12 due to the rotation of the auxiliary mirror 10 offset each other.
Specifically, by using servo control or the like capable of providing feedback, the displacement of the rotational angle of the auxiliary mirror 10 is measured by using the angle sensor 52, while the displacement of the rotational angle of the dynamically compensating balancer 11 is measured by using the angle sensor 53. The values measured with the angle sensors 52 and 53 are outputted as signals, and control is provided such that these output signals assume desired values.
FIG. 16 is a block diagram for explaining a method of controlling the above-described apparatus for driving an auxiliary mirror.
In FIG. 16, reference numeral 54 denotes a transfer function which expresses the dynamic characteristic of the auxiliary mirror 10. In the transfer function 54, a torque for driving the auxiliary mirror 10 is used as its input, and the transfer function 54 outputs the angle of the auxiliary mirror 10. Reference numeral 55 denotes a transfer function which expresses the dynamic characteristic of the dynamically compensating balancer 11. In the transfer function 55, a torque for driving the dynamically compensating balancer 11 is used as its input, and the transfer function 55 outputs the angle of the dynamically compensating balancer 11.
Numeral 58 denotes a stabilizing filter for providing control such that the difference between the angle of the auxiliary mirror 10 detected by the angle sensor 52 and an auxiliary-mirror-angle command signal becomes 0. Numeral 56 denotes an actuator driver for calculating the torque to be imparted to the actuator (not shown) for adjusting the angle of the auxiliary mirror 10 on receiving an output from the stabilizing filter 58.
Numeral 59 denotes a stabilizing filter for providing control such that the difference between the angle of the dynamically compensating balancer 11 detected by the angle sensor 53 and a dynamically-compensating-balancer angle command signal becomes 0. Numeral 57 denotes an actuator driver for calculating the torque to be imparted to the actuator (not shown) for adjusting the angle of the dynamically compensating balancer 11 on receiving an output from the stabilizing filter 59.
Next, a description will be given of the operation of the apparatus shown in FIG. 16.
First, an auxiliary-mirror-angle command signal and a dynamically-compensating-balancer angle command signal are given in order to incline the angles of the auxiliary mirror 10 and the dynamically compensating balancer 11.
The auxiliary-mirror-angle command signal is a signal in which the angle to which the designer intends to incline the auxiliary mirror 10 with respect to the reference plane is converted to a signal, while the dynamically-compensating-balancer angle command signal is a signal in which the angle to which the designer intends to incline the dynamically compensating balancer 11 with respect to the reference plane is converted to a signal. These two command signals are periodical, and are signals whose phases are opposite to each other.
In the auxiliary mirror 10, if the auxiliary-mirror-angle command signal is given thereto, the difference between the same and the angle signal of the auxiliary mirror 10 detected by the angle sensor 52 is calculated, and is transmitted to the stabilizing filter 58.
In the stabilizing filter 58, control is effected such that the difference between the angle signal of the auxiliary mirror 10 and the auxiliary-mirror-angle command signal becomes 0, so that a calculation for correcting the inclination of the auxiliary mirror 10 is made, and the result is transmitted to the actuator driver 56.
Upon receiving the result, on the basis of the result the actuator driver 56 calculates the torque for driving the actuator (not shown) for adjusting the angle of the auxiliary mirror 10, so as to drive the actuator (not shown).
Consequently, the angle of the auxiliary mirror 10 changes, so that the angle is detected by the angle sensor 52, and the above-described control is continued until the difference between the angle signal of the auxiliary mirror 10 and the auxiliary-mirror-angle command signal becomes 0 or assumes a value which can be regarded as 0.
Meanwhile, in the dynamically compensating balancer 11, if the dynamically-compensating-balancer angle command signal is given thereto, the difference between the same and the angle signal of the dynamically compensating balancer 11 detected by the angle sensor 53 is calculated, and is transmitted to the stabilizing filter 59.
In the stabilizing filter 59, control is effected such that the difference between the angle signal of the dynamically compensating balancer 11 and the dynamically-compensating-balancer angle command signal becomes 0, so that a calculation for correcting the inclination of the dynamically compensating balancer 11 is made, and the result is transmitted to the actuator driver 57.
Upon receiving the result, on the basis of the result the actuator driver 57 calculates the torque for driving the actuator (not shown) for adjusting the angle of the dynamically compensating balancer 11, so as to drive the actuator (not shown). Consequently, the angle of the dynamically compensating balancer 11 changes, so that the angle is detected by the angle sensor 53, and the above-described control is continued until the difference between the angle signal of the dynamically compensating balancer 11 and the dynamically-compensating-balancer angle command signal becomes 0 or assumes a value which can be regarded as 0.
By adopting the configuration such as the one shown in FIG. 16, angle command signals whose phases are opposite to each other are given to the auxiliary mirror 10 and the dynamically compensating balancer 11. Hence, the auxiliary mirror 10 and the dynamically compensating balancer 11 are tilted with mutually opposite phases. In addition, since the driving reaction force occurring due to the tilting of the auxiliary mirror 10 and the driving reaction force occurring due to the tilting of the dynamically compensating balancer 11 are identical in magnitude, and their directions are opposite, the driving reaction force ceases to occur in the mounting base 12.
Next, a description will be given of a method for suppressing the deflection of the auxiliary mirror 10 due to its own weight.
If the auxiliary mirror 10 has a large aperture and a large weight, the auxiliary mirror 10 deflects due to its own weight. The manner in which it deflects depends on the inclination of the auxiliary mirror 10.
If the auxiliary mirror 10 has a particularly large aperture and a very large weight, it is necessary to suppress the deflection of the auxiliary mirror 10 due to its own weight.
FIGS. 17A and 17B are cross-sectional views illustrating a mechanism for supporting the auxiliary mirror 10 provided for suppressing the deflection due to the gravity in a conventional auxiliary mirror, as shown in, for instance, Yasumasa Yamashita: "Reflecting Telescope" (University of Tokyo Press, 1992).
Specifically, the auxiliary mirror 10 is segmented into a plurality of blocks, and the weight of each of the blocks themselves is further separated into a component parallel to the auxiliary mirror 10 (a component perpendicular to the optical axis of the auxiliary mirror 10) and a component perpendicular to the auxiliary mirror 10 (a component parallel to the optical axis of auxiliary mirror 10). A supporting mechanism for suppressing the positional deviation due to the weight of the auxiliary mirror 10 itself is provided for each component.
FIG. 17A is a cross-sectional view illustrating the operation in the direction of the optical axis of the auxiliary mirror 10 (the direction perpendicular to the auxiliary mirror 10), and FIG. 17B is a cross-sectional view illustrating the operation in a direction perpendicular to the optical axis (the direction parallel to the auxiliary mirror 10).
In FIGS. 17A and 17B, reference numeral 10 denotes the auxiliary mirror; 12 denotes the mounting base for fixing the auxiliary mirror 10; 31 and 32 denote link mechanisms for supporting the load of the auxiliary mirror 10 in the direction of its optical axis; 33 denotes a counter weight for canceling a component, acting in the direction of the optical axis, of the weight of the auxiliary mirror 10 itself; 34 denotes a fulcrum of the link mechanism 31; 41 and 42 denote link mechanisms for supporting the load of the auxiliary mirror 10 in the direction perpendicular to its optical axis; 43 denotes a counter weight for canceling a component, acting in the direction perpendicular to the optical axis, of the weight of the auxiliary mirror 10 itself; and 44 denotes a fulcrum of the link mechanism 41.
Next, a description will be given of the operation. In a telescope having a large mirror surface, since the weight of the mirror itself is large, the deformation due to its own weight cannot be ignored. To reduce the deformation due to its own weight, the weight must be supported by being distributed at a multiplicity of supporting points, and a function must be provided whereby its supporting force changes in correspondence with the elevation angle of the telescope.
If it is assumed that the weight of the block itself is W, and the weight of the counter weight 43 itself is Wc when the auxiliary mirror 10 is segmented into a plurality of blocks, FIG. 17A shows that when the elevation angle of the auxiliary mirror 10 is .theta., its component in the optical-axis direction is Wsin.theta., and that the optical-axis component of the force generated by the counter weight 33 and amplified by the link mechanisms 31 and 32 is Wc(s.sub.2 /s.sub.1)sin.theta..
It should be noted that s.sub.1 is the distance from the fulcrum 34 of the link mechanism 31 to the point of application, and s.sub.2 is the distance from the fulcrum 34 to the center of gravity of the counter weight 33.
Consequently, if the dimensions of the link mechanisms and the mass of the counter weight 33 are selected such that the formula W=Wc(s.sub.2 /s.sub.1) is satisfied, it becomes possible to offset the optical-axis-direction component of the weight of the auxiliary mirror itself irrespective of the elevation angle of the telescope. Hence, it becomes possible to suppress the deflection of the auxiliary mirror 10 in the optical-axis direction due to its own weight.
FIG. 17B shows that the component, perpendicular to the optical axis, of the auxiliary mirror 10 is Wcos.theta., and that the component, perpendicular to the optical axis, of the force generated by the counter weight 43 by means of the link mechanisms 41 and 42 is Wc(s.sub.2 /s.sub.1)cos.theta..
It should be noted, however, that s.sub.1 is the distance from the fulcrum 44 of the link mechanism 41 to the point of application, and s.sub.2 is the distance from the fulcrum 44 to the center of gravity of the counter weight 43.
Consequently, for exactly the same reason as that for the optical-axis direction, if the dimensions of the link mechanisms and the mass of the counter weight 43 are selected such that the formula W=Wc(s.sub.2 /s.sub.1) is satisfied, it becomes possible to offset the component, perpendicular to the optical axis, of the weight of the auxiliary mirror itself irrespective of the elevation angle of the telescope. Thus, by disposing a multiplicity of mechanisms, such as those shown in FIGS. 17A and 17B, on the auxiliary mirror, it is possible to automatically vary the supporting force without causing the supporting force to be concentrated on a particular point of application and irrespective of the elevation angle of the telescope.
With the above-described apparatus, the vibration of the mounting base 12 becomes a problem. If the mounting base 12 vibrates, it becomes difficult to accurately determine the inclination of the auxiliary mirror 10 and the dynamically compensating balancer 11, and the transition time is prolonged.
In the event that a time lag has occurred between the torques generated by the actuators (not shown) for tilting the auxiliary mirror 10 and the dynamically compensating balancer 11 by imparting torques thereto, the driving reaction force occurring in the mounting base 12 by tilting the auxiliary mirror 10 and the driving reaction force occurring in the mounting base 12 by tilting the dynamically compensating balancer 11 cease to offset each other, possibly swaying the mounting base 12.
In addition, if the angle sensors are installed on the mounting base 12, it means that the detected angle of the auxiliary mirror 10 is the one which is detected from the mounting base, and the auxiliary mirror 10 is controlled in such a manner as to tilt the auxiliary mirror 10 to a designated angle from the mounting base 12.
At this time, the design is made so that the mounting base and the reference plane are located in parallel.
The angle at which the auxiliary mirror 10 is tilted must be controlled in such a way as to be tilted to a designated angle from the reference plane. Therefore, if the inclination of the mounting base and the inclination of the reference plane differ from each other, there is a problem in that the angle cannot be detected adequately when the angle of the auxiliary mirror from the reference plane is detected from the mounting base.
The aforementioned problem will be described with reference to FIG. 18.
FIG. 18 is an explanatory diagram illustrating the fact that it becomes impossible to control the angle of the auxiliary mirror due to the swaying of the mounting base in a conventional apparatus for controlling the driving of an auxiliary mirror.
In FIG. 18, reference numeral 10 denotes the auxiliary mirror; 11, the dynamically compensating balancer; and 12, the mounting base. The mounting base 12 is disposed in such a manner that the angle of the auxiliary mirror 10 with respect to the mounting base 12 and the angle of the auxiliary mirror 10 with respect to the reference plane are identical.
Reference numeral 13 denotes a supporting structure for supporting the mounting base 12 at the reference plane. Since the supporting structure 13 does not completely fix the mounting base at the reference plane, the mounting base 12 sways in correspondence with the rigidity of the supporting structure 13 if the difference between the driving reaction force occurring in the mounting base 12 due to the tilting of the auxiliary mirror 10 and the driving reaction force occurring in the mounting base 12 due to the tilting of the dynamically compensating balancer 11 becomes excessively large.
As shown in FIG. 18, the motion of the auxiliary mirror 10 and the motion of the dynamically compensating balancer 11 are not completely independent, and have a characteristic that they interfere with each other via the supporting structure which supports them. Although the effect is small in the case of a relatively small-size apparatus for controlling the driving of an auxiliary mirror, the rigidity of the supporting structure relatively declines in the case of a large-size auxiliary mirror, so that the motion of the auxiliary mirror and the dynamically compensating balancer induces the motion of the supporting structure. As a result, the effect of the motion of the two members on changes of their respective angles becomes large.
Reference numeral 52 denotes the angle sensor for detecting the angle of the auxiliary mirror 10, and numeral 53 denotes the angle sensor for detecting the angle of the dynamically compensating balancer 11, the angle sensors 52 and 53 being mounted on the mounting base 12.
In FIG. 18, the mounting base 12 is not completely fixed, and is installed on the ground or the like by means of the supporting structure 13 which has finite rigidity.
In the spatial chopping method, since the auxiliary mirror 10 receives light from the main mirror (not shown) fixed in the reflecting telescope, if the inclination of the main mirror (not shown) is set as the reference plane, it is necessary to adequately control the relative angle between the main mirror (not shown) and the auxiliary mirror.
For this reason, the relative angle between the main mirror (not shown) and the auxiliary mirror 10 is controlled by installing the mounting base 12 in parallel with the inclination of the main mirror (not shown) and by providing the angle sensors on the mounting base 12.
Here, it should be noted that since the angle sensors are provided on the mounting base 12, the angle of displacement between the auxiliary mirror 10 and the dynamically compensating balancer 11 is one which is measured not from the reference plane but from the mounting base 12.
It is assumed that the mounting base 12 is stationary with respect to the reference plane, and that only the actuator (not shown) for adjusting the inclination of the auxiliary mirror 10 is generating torque at this time, thereby rotating the auxiliary mirror 10 clockwise.
The mounting base 12 rotates counterclockwise due to the driving reaction force occurring due to the rotation of the auxiliary mirror 10.
Consequently, the conventional controlling apparatus, which is based on the assumption that the mounting base 12 does not become offset from the reference plane, judges that such a relative displacement has occurred that the dynamically compensating balancer 11 has undergone clockwise rotation, as it were.
Since the control system for controlling the angle of the auxiliary mirror 10 and the angle of the dynamically compensating balancer 11 is configured as shown in FIG. 18, by rotating the dynamically compensating balancer 11 counterclockwise the conventional control system operates in such a manner as to cause the angle of the dynamically compensating balancer to approach the angle designated by the dynamically-compensating-balancer angle command signal.
This force for rotating the dynamically compensating balancer 11 counterclockwise now constitutes a driving reaction force for rotating the mounting base 12 clockwise, so that the control system operates in such a manner as to allow that force to assume a value which designates a relative displacement by rotating the auxiliary mirror 10 clockwise.
In other words, as the mounting base 12 vibrates, if an attempt is made to control either one of the auxiliary mirror 10 or the dynamically compensating balancer 11, an influence is exerted on the other, so that the tilting of the auxiliary mirror 10 and that of the dynamically compensating balancer 11 interfere with each other.
Thus, with the conventional control system, despite the fact that the motion of the auxiliary mirror 10 and that of the dynamically compensating balancer 11 interfere with each other, the control of their angles is respectively provided independently. Hence, there has been a problem in that the vibration of the mounting base 12 cannot be suppressed due to the above-described phenomenon in the case where the mounting base 12 vibrates.
Additionally, since it becomes impossible to maintain the relationship of parallelism between the mounting base 12 and the reference plane due to the swaying of the mounting base 12, there has been a problem in that the reliability of output values of the angle sensors declines, and that the transition time is prolonged.
In addition, the conventional method of supporting an auxiliary mirror of a reflecting telescope makes it possible to provide satisfactory performance in the case of a telescope in which the auxiliary mirror 10 is used by being fixed.
However, with the telescope of the type in which the auxiliary mirror 10 is repeatedly tilted at high speed, wide-band servo control for controlling the displacement of the tilting angle of the auxiliary mirror is indispensable. For that reason, the structure for supporting the auxiliary mirror 10 which is driven must be made rigid.
If the structure for supporting the auxiliary mirror 10 is arranged to be rigid, an excessively large driving force is required for driving the auxiliary mirror 10. Consequently, with the supporting mechanism which is comprised of a multiplicity of small component parts, as shown in FIGS. 17A and 17B, the link mechanisms each provided with a counter weight vibrate, so that there has been a problem in that the servo control system causes resonance in the supporting mechanisms.
In addition, in a case where the auxiliary mirror 10 is inclined to a predetermined angle, sensors are required which are capable of accurately measuring a region in the vicinity of the predetermined angle.
If it is assumed that the angles between which the auxiliary mirror 10 is tiltably moved are .theta..sub.1 and .theta..sub.2 (where .theta..sub.1 &gt;.theta..sub.2), the range of measurement by the measuring means should preferably be greater than .theta..sub.1 and smaller than .theta..sub.2.
In other words, requirements of the sensor for measuring the angle are that the measurement range should be wider than the angular range in which the auxiliary mirror 10 is tiltably moved, and that the detection accuracy in the vicinity of the angle at which the auxiliary mirror 10 is held should be high.
However, a wide extent of the measurement range and a high level of detection accuracy are generally in a reciprocal relationship.
That is, the measurement range and the detection accuracy are in such a relationship that if the measurement range is made wide, the detection accuracy declines, whereas if the detection accuracy is made high, the measurement range becomes narrow.
In addition, even if a multiplicity of sensors respectively having narrow but different detection ranges and high detection accuracy are arranged to detect a wide range, it becomes necessary to correct the positional deviation of heads (not shown) of the multiplicity of sensors. Further, the number of lines or wires of the wiring for transmitting the signals outputted from the individual sensors increases substantially.
Moreover, in a case where the direction of the drive rotation axis of the auxiliary mirror 10 is arbitrarily changeable, the auxiliary mirror 10 can be tilted in various directions.
In this case, as the direction of the rotation axis changes, the distance from the drive rotation axis of the auxiliary mirror 10 to the angle sensor changes. Hence, if the direction of the rotation axis changes, both its detection range and a region which is to be detected with high accuracy also change simultaneously even in the case of the same angle sensor.
Accordingly, the region of angles for which high detection accuracy is required also changes, so that it is not effective to install an angle sensor having high detection accuracy by being offset in advance from a neutral position.
Namely, with the conventional angle sensors for detecting the angle of the auxiliary mirror 10, only either an angle sensor having high detection accuracy or an angle sensor having a wide measurement range is used, so that there has been a drawback in that either the high level of detection accuracy or the wide extent of the measurement range must be sacrificed.